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It seems to me that every melody can be assigned chords. Although different people may assign different chords, in many cases, only certain chords (a small subset of all possible chord choices) seem to fit a melody better than others.

What are the rules that determine the harmony (possible chords) of a melody? What is their origin? Are they only the result of arbitrary cultural-historical choices, or are they rooted in psychology, neuroscience, and math (frequency-ratios)?

Related questions:

  1. What is the relationship between the melody line and the rhythm chords? That question largely overlaps with mine. My question is more theoretical, and focuses more on the origin of the rules.

  2. Is it possible to find the correct chords from melody notes alone? The answers to that question mention a few rules.

  3. Harmony analysis program That question suggests that the rules may be formulated.

  4. What exactly should I have to learn to understand why certain combination of chords are harmonic when played in a sequence? That question is concerned with the "horizontal" aspect of harmony, while I am asking about the "vertical" aspect (but then maybe vertical and horizontal are inseparable).

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The answers to your question lie in studying the music theory of what is called "Common Practice" in the history of Western music. It is usually the subject of a two-year curriculum in music colleges. You can certainly study it on your own out of textbooks, but it is not something that can be explained in a couple of short posts on a site like this one. –  Wheat Williams Dec 8 '13 at 22:17
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Your assertion that "every melody has chords which most people would agree on" is certainly not the case. If you study jazz or classical music, you will understand that what jazz musicians and classical composers often do is to figure out how to harmonize a given melody with many different chord progressions. In jazz, this is called "chord substitution". –  Wheat Williams Dec 8 '13 at 22:18
    
Another short answer: pick harmonies that sound nice, or enhance the listener's anticipation of the upcoming changes. –  Carl Witthoft Dec 9 '13 at 12:43
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The book This is Your Brain on Music goes into detail about the issues you're asking about. amazon.com/gp/aw/d/1400033535/… –  Kevin Dec 9 '13 at 18:31
    
Question, while worthy, is much too broad and needs to be split up into separate sections. –  Kevin Johnsrude Jul 14 at 17:39

4 Answers 4

Your question is a bit too open-ended to be answered completely and all the comments that have been made already give you useful pointers.

Said simply: your ear has been trained by what you have heard over the years. When you hear a few notes, your brain will want to make sense of it, fall back onto its feet, the same way that you make sense of a few dots and lines on a piece of paper that evoke a shape with which you are familiar. You will likely hear a few scales that you have heard over and over and that could go along with the few notes your played: you are essentially connecting the dots by finding scales that share (most of) these notes that were played.

Now successions of chords belong to these scales that will incorporate, implicitly or explicitly the notes that are being played, and this progression of chords will likely sound "right", "make sense", some more than others depending where (you think) the melody is going, and how each chord resolve into the next one.

These harmonies are essentially your interpretation of the melody that will obey some music rules that you are accustomed to.

Now many major steps in the history of music are made when composers stretch the comfort level of their society and introduce new harmonies that do not "make sense" to their peers but progressively make their ways into people's mind/taste/subconscious until they become harmonies accepted more widely. Many of the harmonies that obviously go well with a melody today to most people's standard didn't necessarily make as much sense a few centuries ago.

Depending on what style you are after, classical, jazz, etc., there are great books and classes to help you learn about the harmonies that will go well with the melody for a specific style. A noble quest...

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I believe you should be using the word harmonies in place of harmonics. –  Basstickler Dec 18 '13 at 1:45
    
Thank you, I will make the correction. You are entirely correct. I am biased by my DSP background :-) –  Lolo Dec 18 '13 at 2:33
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I'm glad you didn't think I was just being a stickler –  Basstickler Dec 18 '13 at 4:22
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No. The quest for accuracy is a noble one. –  Lolo Dec 18 '13 at 5:36

Part of this can be answered by the idea of Function. Within the Western music tradition chords serve a function, that is they play a role. The most commonly known term from this thought process is the Dominant function, built on the V of the key. The Dominant chord is named such because it has the most tension and most desire to resolve back to the Tonic, or I chord. It is Dominant in that it demands to be resolved and therefore Dominates the harmonic progression. The IV is known as the Pre-Dominant and is frequently used to set up the Dominant chord. As an example, I | IV | V | I | is very common, or I | vi | IV | V | All of the chords have a functional name and different uses (like Pre-Dominant is not played exclusively before the Dominant) but that is, as others have suggested, quite a long discussion.

An interesting fact that seems less known or thought about could answer some of your question as well. It is common knowledge that within a given key there are 3 major chords but people don't always realize that all 7 notes of the scale can be harmonized with at least one of those 3 chords. This is why any diatonic melody (within the scale) can be harmonized with some combination of I, IV and V chords. If you add function to the mix, then the chord choices become more obvious. As an example, when notes within the melody are dissonant, you are likely to have the Dominant chord.

As others have suggested in their answers, tradition and cultural tendencies play a very large role. As the tradition evolved, people began to play with the 'rules' of Function. Composers would have non-diatonic melodies (consisting of notes outside the scale), which would require non-diatonic harmonies. Modal Mixture/Borrowing is a fun one that has continued to be used by seemingly all expansions/genres of western music. Modal Mixture/Borrowing consists of 'borrowing' a chord and/or melodic note from a parallel key (in A major you could borrow a chord from A minor). The Blues is a good example as well. The Blues is built on Dominant 7 chords. Using all Dominant 7 chords is playing with the idea of Function. Instead of the Dominant 7 being the Functional Dominant, it is the harmonic texture. The role of Dominant is still fulfilled by the V7 but the I7 and IV7 are not Functionally Dominant, as they do not have the same desire to resolve to the Tonic (the I chord). The Function of V is further played with by 'stressing' the Dominant. In the standard Blues progression the first V chord is followed by a IV chord, thereby denying its Function. The V only appears again in the turnaround, the last bar, and then fulfills its Function as Dominant to bring the progression back to the beginning. (Sorry for the extended examples but I think they help illustrate the point)

So these cultural tendencies, such as the Blues, lead us to feel certain chord progressions are obvious or the 'right' choice. If you gave a Blues melody to someone that had only heard Classical music up to 1750ish, they would not have the cultural experience to know which chords would accompany this. Jazz musicians use the ii chord as a Pre-Dominant. Aside from the differences in harmonic language, this would mean that the 'obvious' choice to the Classical composer is going to be different than that of the Jazz composer 99% of the time, just based on the cultural norm. Guys like Thelonious Monk (Jazz) and Claude Debussy (Classical in the Romantic era) are great examples of harmonizing melodies in unexpected ways.

There is sort of a scientific explanation but I don't believe there is an official theory per se. Mathematically, frequency determines pitch and when two pitches are played simultaneously, their consonance/dissonance (tension) can be measured in terms of a ratio. Unison is the most consonant 1:1, with the octave next 2:1, then the fifth 3:2, and so forth. The major chord is perceived as more consonant than minor, which often translates to happy/sad, because it is more consonant, which can be proven mathematically. Scales, and thereby keys, are mathematically determinable and naturally occurring. They are determined by the harmonic overtones produced by a single note, which I will not try to define as I am already making quite a lengthy answer. Nevertheless, scales do occur naturally and do pervade all forms of melodic music, including the Eastern traditions as well as indigenous tribes that had seemingly had no outside contact since the onset of music theory.

This next part is more conjecture, as I am not studied in Psychology or Neuroscience. I believe that once a key is established, our brains interpret that as home base and anything else is compared to that, which gives it a sense of consonance or dissonance. The further removed from the home base, the more dissonant it sounds, even if you play a consonant chord. The Dominant triad consists only of notes that are not in the Tonic, making it have the most desire to resolve back to Tonic. The Dominant also contains what has become known as the Leading Tone, the 7th degree of the scale. It is a half-step below the root of the Tonic and by this thought process, it is the most dissonant note in the scale. (In case there is any confusion: being 'further removed', as I described it, does not mean distance from a note. Combining this with the mathematical side, though a half-step is 'closer' to the root, it is a more dissonant interval than the whole step, making it 'further removed')

So we combine cultural tendencies and conditioning with sets of frequencies' ratios equaling consonance vs. dissonance and potentially my conjecture on our brains' interpretation of being in a key and to some extent you can see why there are 'right' or 'obvious' choices for a given melody. Cultural exposure will lead to melodic tendencies, which, through the same exposure, will have seemingly 'correct' harmonizations. So even if you are coming up with non-diatonic melodies, which means not naturally occurring, it is likely due to cultural conditioning, which has also provided you with a means of harmonizing it.

As a composer, I always try to break free of the obvious.

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Examining the history of Western music might be helpful here. Contrary to what you might expect, polyphony, or multiple independent melodies sounding simultaneously, came before homophony, or melody with harmony/chords. The first examples of Western music were just single-voice melodies — think Gregorian chanting. Since each octave had the same pitches, and since it made sense to end on the same pitch you started on, the octave was divided in various ways, forming modes. For psychological reasons, it sounded better for notes to move to neighboring notes rather than leaping large intervals all the time. After a while, people figured out that sounding the root note as a "drone" made everything a bit more interesting due to the (explicit) appearance of intervals. Some of the intervals were dissonant (unstable), while others were consonant (stable), and again for psychological reasons, the human ear wanted to hear the dissonances resolve to consonances. Eventually, polyphonic voicing became more common; the interesting relationship between consonant and dissonant intervals was still being explored, but now the drone voice (along with possibly several others) started to move independently. Right around (or after) the Baroque period, people started to notice the reoccurrence of specific vertical note patterns, often used for rhetorical effect (cadences, etc.). These patterns were condensed into "chords", and thus homophonic music was born.

Today, when we write melodies, we think in terms of harmony because it's an easy and useful abstraction that we've built up over the raw building blocks of modes and intervals. Chord progressions "just work", and you can use them to great emotional effect without doing too much extra work. That's not the case for all genres of music; jazz players, for example, often work with consonant/dissonant intervals directly, leaving it to others to figure out the "chords" ex post facto. (Hence the crazy chord names.)

Let's look at an example chord progression: I-IV-V-I, the basic outline of many melodies. The I chord is composed of two intervals, a major and minor 3rd (C-E and E-G). Note that these intervals weren't always considered stable, but sometime in the Renaissance (or earlier) this perception changed. From the upper minor 3rd, you only need to move a half step and a whole step to get to an arrangement of a perfect 4th (a very stable interval) and another major 3rd (C-F and F-A). From there, simply move down a half step for the bottom note and up another whole step for both upper notes to get an arrangement of a major 6th and yet another major 3rd (B-G and G-B). However, the root note is still in the listener's ear, so you also get the dissonant minor 2nd (B-C) in addition to the consonant perfect 5th (C-G). If you're feeling crazy, you can even keep the F to create a dissonant tritone that sounds like it must resolve (B-F)! Finally, from there, we move a few more steps and we're back to our original chord, C-E-G. This system allows us to move a) in half or whole steps b) between consonant and dissonant intervals and c) creates a pattern through which we start somewhere, move somewhere else, and end up back where we started. Could we use another system? Sure, we could start with C-F-Bb or something for a chord composed of a different set of stable intervals in a different mode, but this would require creating a lot of new chords and in general thinking pretty hard.

That's my layman's understanding of it, anyway.

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your 4 or 5 questions are enough to keep you busy for a few lifetimes, and are questions you will find in the study of harmony (long study), music history (long history), and duh, neuroscience and math, (even longer studies) the last two of which I know nothing about as I am a musician, not a scientist.

What are you trying to achieve? Understanding harmony from a scientific point of view isn't the same thing as understanding it from the traditional study of harmony taught in a conservatory. You could say that the latter study is the science of the musician. Have a look at books such as Jean Philippe Rameau's 'Treatise on Harmony' to see an example of a musician who was as scientific as a musician could ever be while still remaining a musician. Also even earlier important theorists, such as Thomas Morley or even earlier,such as Gioseffo Zarlino.

In music you have to use your ears a lot too, not just your brains. In science they don't use ears, because music is primarily the realm of musicians. Science, for the most part, doesn't teach anything about music to a musician, that he really needs to know. For example, during the Renaissance, composers wrote a major triad at the end of a piece in a minor key. They said the major third is more 'perfect' than a minor third. This was called a 'picardy third'.

If science would have to tell you why they wrote a major third instead of minor, I doubt they could. But musiciana could 'feel' why. The study of music such as that done by serious musicians, is scientific enough, i.e. long enough, to make any of them want to look for answers in neuroscience. It's like a racing driver who learned how to race and how to disassemble a car engine, who wants to race and win. Would he be learning about flying into space at the same time? I doubt it. It's not relevant to him, as he looks for results on the racing track rather than into space. I believe a musician is very much the same.

So it depends on what you are trying to do, and who you are: a musician, or a scientist?

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I agree; the OP question is a bit too broad and AFAIK science still has no complete answer. –  Anthony Dec 11 '13 at 20:30

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